My friend showed this to me a few days ago...
-1 = -1
-1/1 = 1/-1
sqrt(-1/1) = sqrt(1/-1)
sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)
sqrt(-1)*sqrt(-1) = sqrt(1)*sqrt(1)
-1 = 1
In case you are wondering, there is in fact an error in the proof. The operation done between the third and fourth lines is not possible.
Thursday, February 21, 2008
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4 comments:
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God is love.
Love is blind.
Ray Charles is blind.
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Anthony, this makes absolutely no sense to me. You are a geek. Bless your heart.
Actually, the error isn't in the third line. That's a completely plausible assumption:
(a/b)^(x) = (a^x)/(b^x)
where a=1 and b=-1 and x=(1/2) (a and b vice versa'd on the other side of the equation)
Which means the fourth line can be rewritten as:
i/1 = 1/i
i*i=1*1
bringing us th final conclusion of:
-1 = 1
Where the math calls apart is assuming that sqrt(1) = 1
It actually equals plus or minus 1.
And seeing as the only answer where the square of i and the square root of 1 coincide is at -1 we see that the math actually falls apart for a different reason.
Here's another one:
in Electrical Engineering the imaginary number j = sqrt(-1)
j^2 = -1 then j^2 * j^2 = -1 * -1 = 1 right?
But:
1 = sqrt (j^2 * j^2)
1 = sqrt (j^4)
1 = j^2
1 = -1
what went wrong?
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